Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components
Year: 2026
Type: preprint
Abstract: We construct examples of uniformly quasiregular mappings (uqr) acting on a sphere and having Fatou set consisting of infinitely many components. In particular we construct a uqr mapping providing a higher dimensional counterpart for the polynomial $z \mapsto z^2 - 1$ acting on the extended complex plane $\hat{\mathbb{C}}$.
Source: arXiv (Cornell University)
Authors: Martin, Gaven, Peltonen, Kirsi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166534028